On the characterization of D-preinvex functions

In (J. Inequal. Appl. 2006:9532, 2006), Peng and Zhu discussed interrelations among D-preinvexity, D-semistrict preinvexity, and D-strict preinvexity for vector-valued functions. In this note, we show that the same results or even more general ones can be obtained under weaker assumptions. We also give a new characterization of D-preinvexity and D-semistrict preinvexity under mild conditions.